Generative modeling of natural images has seen significant progress, but large-scale foundation models raise concerns about environmental impact, privacy, and biases. This motivates investigating more efficient and interpretable generative models. This work proposes a simple latent parametric generative model focused on realistic face generation, a domain that has seen success with neural networks. The model uses a low-dimensional latent representation from a pre-trained autoencoder, and proceeds in two stages: (1) modeling the latent distribution as a mixture of multivariate Gaussians trained on a limited dataset, and (2) generating low-rank random codes from this prior and remapping them using nearest neighbor matching. Comparative experiments demonstrate the advantages of the proposed approach.